The lifespans of seals in a particular zoo are normally distributed. The average seal lives $14.3$ years; the standard deviation is $3.1$ years. Use the empirical rule (68-95-99.7%) to estimate the probability of a seal living between $8.1$ and $20.5$ years.
Answer: $14.3$ $11.2$ $17.4$ $8.1$ $20.5$ $5$ $23.6$ $95\%$ We know the lifespans are normally distributed with an average lifespan of $14.3$ years. We know the standard deviation is $3.1$ years, so one standard deviation below the mean is $11.2$ years and one standard deviation above the mean is $17.4$ years. Two standard deviations below the mean is $8.1$ years and two standard deviations above the mean is $20.5$ years. Three standard deviations below the mean is $5$ years and three standard deviations above the mean is $23.6$ years. We are interested in the probability of a seal living between $8.1$ and $20.5$ years. The empirical rule (or the 68-95-99.7 rule) tells us that $95\%$ of the seals will have lifespans within 2 standard deviations of the average lifespan. The probability of a particular seal living between $8.1$ and $20.5$ years is ${95\%}$.